Answer
$x^2-4x+3=0$
Work Step by Step
Given the quadratic equation $ax^2+bx+c=0,$ the sum and product of its roots are given by the following ratios:
\begin{align*}
\text{Sum: }&-\dfrac{b}{a}
\\\\
\text{Product: }&\dfrac{c}{a}
.\end{align*}
Given that the sum is $
4
$ and the product is $
3
,$ then
\begin{align*}
\text{Sum: }\\
-\dfrac{b}{a}&=4
\\&=-\dfrac{-4}{1}
\\\\
\text{Product: }\\
\dfrac{c}{a}&=3
\\&=
\dfrac{3}{1}
.\end{align*}
Hence, $a=
1
,$ $b=
-4
,$ and $c=
3
.$ The quadratic equation that satisfies the given sum and product is
\begin{align*}
x^2-4x+3=0
.\end{align*}